

A097062


Interleave 2*n+1 and 2*n1.


6



1, 1, 3, 1, 5, 3, 7, 5, 9, 7, 11, 9, 13, 11, 15, 13, 17, 15, 19, 17, 21, 19, 23, 21, 25, 23, 27, 25, 29, 27, 31, 29, 33, 31, 35, 33, 37, 35, 39, 37, 41, 39, 43, 41, 45, 43, 47, 45, 49, 47, 51, 49, 53, 51, 55, 53, 57, 55, 59, 57, 61, 59, 63, 61, 65, 63, 67, 65, 69, 67, 71, 69, 73, 71, 75, 73, 77, 75, 79, 77, 81, 79, 83, 81, 85, 83, 87, 85
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OFFSET

0,3


COMMENTS

Partial sums are A097063, whose pairwise sums are A002061.
Binomial transform is A097064.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

G.f.: (12*x+3*x^2)/((1x^2)*(1x)).
a(n) = (2*n1)/2 + 3*(1)^n/2.
a(n) = 2*(n1)  a(n1), with a(0)=1.  Vincenzo Librandi, Nov 16 2010
a(n) = n  2 + 3*((n1) mod 2).  Lechoslaw Ratajczak, May 21 2021
a(n) = a(n1)+a(n2)a(n3).  Wesley Ivan Hurt, May 21 2021


MATHEMATICA

LinearRecurrence[{1, 1, 1}, {1, 1, 3}, 100] (* Amiram Eldar, May 21 2021 *)


PROG

(Haskell)
import Data.List (transpose)
a097062 n = a097062_list !! n
a097062_list = concat $ transpose [a005408_list, (1) : a005408_list]
 Reinhard Zumkeller, Apr 16 2015
(PARI) a(n)=(2*n1)/2+3*(1)^n/2 \\ Charles R Greathouse IV, Oct 07 2015
(PARI) Vec((12*x+3*x^2)/((1x^2)*(1x)) + O(x^100)) \\ Altug Alkan, Nov 13 2015
(Magma) [(2*n1)/2 + 3*(1)^n/2 : n in [0..100]]; // Wesley Ivan Hurt, May 22 2021


CROSSREFS

Cf. A005408, A097063, A097064.
Sequence in context: A089654 A233526 A344674 * A350948 A324894 A200498
Adjacent sequences: A097059 A097060 A097061 * A097063 A097064 A097065


KEYWORD

sign,easy


AUTHOR

Paul Barry, Jul 22 2004


STATUS

approved



